Interest rate: Sofie wants to invest $25,000 in a spa that her sister is starting. She will triple her investment in six years. What is the rate of return that Sofie is being promised? (Rounded to the nearest per cent.)
A) 18%
B) 20%
C) 12%
D) 25%

Question

Quizplus · Accepted Answer

To find the interest rate, we can use the formula:

future value = present value x (1 + interest rate)^n

where n is the number of years and future value is three times the present value (25,000).

So,

75,000 = 25,000 x (1 + interest rate)^6

Dividing both sides by 25,000, we get:

3 = (1 + interest rate)^6

Taking the sixth root of both sides, we get:

1.26 = 1 + interest rate

Subtracting 1 from both sides, we get:

interest rate = 0.26 or 26%

However, this is the nominal annual interest rate. To find the effective annual interest rate, we need to use the formula:

effective annual interest rate = (1 + nominal annual interest rate/n)^n - 1

where n is the number of times interest is compounded in a year. We don't know how often interest is compounded in this case, so let's assume it's compounded monthly (12 times a year).

Then,

effective annual interest rate = (1 + 0.26/12)^12 - 1

= 0.199 or 19.9%

Rounding this to the nearest percent, we get 20%. Therefore, the promised rate of return is 20%.

Interest Rate: Sofie Wants to Invest $25,000 in a Spa